The paper is concerned with a doubly infinite vortex array introduced by Weihs (Nature 241:290–291, 1973; in: Wu, Brokaw, Brennen (eds) Swimming and flying in nature, Vol. 2, Plenum Press, New York, 1975) as a model problem employed in order to understand the hydrodynamic and energetic benefits of fish schooling. Weihs considered two different ‘modes’ of swimming: one where the fish swim in anti-phase and one where they swim in phase. The stability properties for the vortex array corresponding to the anti-phase mode of swimming are well understood; but this is not the case for the in-phase mode. A normal mode analysis of perturbations applied to the corresponding vortex array is carried out. The array is found to be always unstable when subjected to general perturbations, but stable solutions exist if all consecutive vortex streets are subjected to the same perturbation.